0

I saw this video recently and it suggests that there is some "magical" reason that there are 360 degrees in a circle and that it is also connected with our number system. My question is:

  1. How did we decide upon our number system (i.e. The base 10 system)? I always believed it was because we have ten fingers to count with.

  2. Is our number system connected with the reason we have 360 degrees in a circle? If so, what is that reason? If not, what significance is there to 360?

tyobrien
  • 3,469
  • I would say you're right about $10$ coming from our number of fingers. $360$ was probably an estimate for the number of days in the year. – Colm Bhandal Aug 02 '15 at 16:32
  • 1
    Sandal-wearing mathematicians sometimes use base $20$. – André Nicolas Aug 02 '15 at 16:34
  • 1
    Purely opinion: The reasons aren't magical. There are 24 hours in a day, so 360 degrees gives us 15 even one-hour timezones. Also, 360 has a LOT of divisors, so it was easy to do math using this number, historically, by hand. Keep in mind, there's also radians and gradians which have 400 ticks instead of 360. As for the number system, it's probably to do with our fingers but there are lots of non base ten systems used by different cultures throughout history. – Race Bannon Aug 02 '15 at 16:35
  • Duplicate of duplicate? http://math.stackexchange.com/questions/340467/why-is-a-full-circle-360%C2%B0-degrees and http://math.stackexchange.com/questions/142735/why-is-a-full-turn-of-the-circle-360%C2%B0-why-not-any-other-number. Found these with a search for why 360 degrees – Ethan Bolker Aug 02 '15 at 16:35
  • 1
    The video itself is, in my opinion, not very enlightening from a mathematical point of view. The significance of $9$ only makes sense in our number system. If we had a base $8$ number system, we'd probably be seeing all sorts of similar patterns emerge with $7$. – Colm Bhandal Aug 02 '15 at 16:38
  • 1
    @RaceBannon agreed about divisors- 360 is highly composite. So is 24, 12 and 60, which makes sense why these crop up so much in measurements. Lots of ways to divide them. See: https://en.wikipedia.org/wiki/Highly_composite_number – Colm Bhandal Aug 02 '15 at 16:40
  • This is a duplicate of this which, in turn, is a duplicate of this, which has an accepted answer. – wltrup Aug 02 '15 at 16:43
  • Okay thanks for the info. Should I go ahead and delete this question? – tyobrien Aug 02 '15 at 16:44

1 Answers1

0

Both are arbitrary, and not everyone uses the same base. I've heard of different civilizations using base 20, computer scientists use base 2 and 16 a lot. Why 10 is so popular I believe is usually said to be because we have 10 fingers.

For 360, the story I've heard is that it is due to astronomy. There are 365 days in a year, but that's kind of an ugly number, so for convenience we change it to 360 which is divisible by 2,3,4,5,6,... a lot of numbers.